This invention relates to limited-angle imaging and especially to reducing the amount of computation time to reconstruct an image using iterative algorithms.
In some situations in industrial x-ray CT (computerized tomography) complete projection data of the object are not available. Projection data in some angular range could be missing due to reasons such as too much attenuation or physical inaccessibility; these situations are depicted in U.S. Pat. No. 4,506,327. An iterative method to reconstruct the object under such circumstances have been reported in that patent and the inventor's other copending patent applications and in published papers authored by the inventor and V. Perez-Mendez; the procedure is shown in FIGS. 1 and 2. The iteration algorithm fills in the missing scan data by utilizing the a priori information on the object. The reconstructed image is transformed back and forth between the object space and the projection space, being corrected in the object space by the a priori information about the object, and in the projection space by the measured projection data. The results in the published papers demonstrated that the iteration algorithm indeed brought about significant improvement in limited-angle imaging.
Typically it takes about 5 to 10 iterations for the reconstructed image to converge. In each iteration the major part of the computer time is spent in the filtered backprojection and the projection operations. Since the projection operation needs to be performed only in the missing views, the computer time on the projection operation will be much smaller than on the filtered backprojection operation if the number of missing views is a small fraction of the total number of views. This condition is usually fulfilled in industrial x-ray CT. Thus the total computer time T to reconstruct the image using the iterative algorithm in FIG. 2 is roughly equal to the number of iterations n times the computer time t for a filtered backprojection operation: T.apprxeq.nt. Since filtered backprojection is the algorithm for reconstructing images in complete-angle x-ray CT, this equation says that the computer time for limited-angle reconstruction is about 5 to 10 times that for complete-angle reconstruction.